Since the diffraction angle is limited by the spatial resolution of the spatial light modulator (SLM), the size of the optical image of the lensless holographic projection with a SLM is very small. Using a divergent spherical beam to illuminate a SLM is an effective method to physically increase the projection angle; nevertheless, the sampling ranges of the existing Fresnel diffraction algorithms with fast Fourier transform keep unchanged. In this paper, a double-sampling Fresnel diffraction algorithm to enlarge the sampling range is proposed when using a divergent spherical beam to illuminate a SLM, and the magnification of the optical image is realized in lensless holographic projection. The hologram can be easily optimized by the Gerschberg-Saxton algorithm. Simulation and experimental results with enlarged optical image are presented successfully.